A-Level Maths: Pure (Year 2) from Udemy

A-Level Maths: Pure (Year 2) is a course for anyone studying A-Level Maths:

This course covers all the second year pure content in A-Level. The course is suitable for all major exam boards, including Edexcel It is also a great course for anyone wanting to learn some more advanced pure maths. This course is intended for purchase by adults.

The main sections of the course are:

- Parametric Equations - where we learn how to express algebraic fractions in partial fractions, a trick used to great effect later in the course.

- Functions in Graphs - where we explore modulus functions, graph transformations, and learn about different types of functions, range and domain.

- Binomial Expansion - here we extend the binomial expansion formula covered in my Pure (Year 1 / AS) course to include negative and fractional powers.

- Radians - we learn about a new way to measure angles, and the amazing things that this facilitates.

- Trigonometric Functions - here we learn about three new trig functions (sec, cosec and cot), and explore the numerous ways that these new functions can be used.

- Trigonometric Identities and Modelling - Here we learn about the compound angle formulae, and look at how these can be used. We also explore harmonic form and learn to use this to model real-world scenarios.

- Differentiation - in this chapter we take the differentiation already learned in the Pure (Year 1 / AS) course to a whole new level. We learn how to differentiate pretty much every type of function we can think of, learning about the chain rule, product and quotient rules, as well as connected rates of change.

- Integration - a giant chapter in which we learn many different techniques to integrate increasing advanced functions. We also explore differential equations.

- Parametric Equations - here we learn about a brand new way to represent a curve, and explore how to use calculus with parametric curves.

- Numerical Methods - here we explore various techniques for finding roots of equations, like x = cosx, that are impossible for find exact solutions to.

- Vectors - here we learn how to work with vectors in 3D, extending what was covered in the previous pure course.

What you get in this course:

Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.

Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these.

Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.

This course comes with:

· A 30 day money-back guarantee.

· A printable Udemy certificate of completion.

· Support in the Q&A section - ask me if you get stuck.

I really hope you enjoy this course.

Woody

What's inside

Learning objectives

Differentiation: chain rule, product rule, quotient rule and more
Integration: reverse chain rule, integration by parts, integration by substitution, differential equations and more
Partial fractions
Graphs and functions
Binomial expansion

Radians
Advanced trigonometry, including sec, cosec and cot, and trigonometric identities
Parametric equations
Vectors
Numerical methods, including iteration and newton-raphson

Differentiation: chain rule, product rule, quotient rule and more
Integration: reverse chain rule, integration by parts, integration by substitution, differential equations and more
Partial fractions
Graphs and functions
Binomial expansion
Radians
Advanced trigonometry, including sec, cosec and cot, and trigonometric identities
Parametric equations
Vectors
Numerical methods, including iteration and newton-raphson

Syllabus

Introduction

Express algebraic fractions in partial fractions.

Two Factors

Two Factors - quiz

Three Factors

Three Factors - quiz

Repeated Factors

Repeated Factors - quiz

Top Heavy Fractions

Top Heavy Fractions - quiz

Proof By Contradiction - Part 1

Proof By Contradiction - Part 1 - quiz

Proof By Contradiction - Part 2

Proof By Contradiction - Part 2 - quiz

Classic Proof By Contradiction 1

Classic Proof By Contradiction 2

Partial Fractions and Proof - Exam Questions

Functions and Graphs

The Modulus Function - Graphs - Part 1

The Modulus Function - Graphs - Part 1 - quiz

The Modulus Function - Graphs - Part 2

The Modulus Function - Graphs - Part 2 - quiz

The Modulus Function - Equations and Inequalities - Part 1

The Modulus Function - Equations and Inequalities - Part 2

Composite Functions

Combining Graph Transformations

Mappings

Mappings - quiz

Domain and Range

Domain and Range - quiz

Composite Functions - quiz

Inverse Functions

Inverse Functions - quiz

Piecewise Functions

Piecewise Functions - quiz

Functions and Graphs Exam Questions

Sequences and Series

Arithmetic Sequences

Arithmetic Sequences - quiz

Arithmetic Series

Arithmetic Series - quiz

Geometric Sequences - Part 1

Geometric Sequences - Part 1 - quiz

Geometric Sequences - Part 2

Geometric Sequences - Part 2 - quiz

Geometric Series

Geometric Series - quiz

Sums to Infinity

Sums to Infinity - quiz

Sigma Notation

Sigma Notation - quiz

Partial Sums

Partial Sums - quiz

Recurrence Relations

Recurrence Relations - quiz

Sequences and Series Exam Questions

Binomial Expansion

The Binomial Expansion Formula

The Binomial Expansion Formula - quiz

Using Binomial Expansion

Using Binomial Expansion - quiz

When The First Term Is Not 1

When The First Term Is Not 1 - quiz

Approximations

Approximations - quiz

Binomial Expansion With Algebraic Fractions

Binomial Expansion With Algebraic Fractions - quiz

Binomial Expansion With Partial Fractions

Binomial Expansion With Partial Fractions - quiz

Binomial Expansion Exam Questions

Radians

Radians - Introduction

Radians - Introduction - quiz

Arc Length

Arc Length - quiz

Sector Area

Sector Area - quiz

Solving Trigonometric Equations In Radians

Solving Trigonometric Equations In Radians - quiz

Small Angle Approximations

Small Angle Approximations - quiz

Using Small Angle Approximations

Using Small Angle Approximations - quiz

Radians Exam Questions

Trigonometric Functions

Sec, Cosec and Cot

Graphs of Sec, Cosec and Cot

Graphs of Sec, Cosec and Cot - quiz

Sec, Cosec and Cot - Proving Simple Identities

Sec, Cosec and Cot - Simple Equations

Sec, Cosec and Cot - Simple Equations - quiz

The Pythagorean Identities

The Pythagorean Identities - quiz

The Pythagorean Identities - Proving Identities

The Pythagorean Identities - Proving Identities - quiz

The Pythagorean Identities - Solving Equations

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Covers the second year pure content in A-Level maths, making it highly relevant for students preparing for A-Level exams

Includes quizzes with questions taken from real A-Level past papers, offering valuable practice for exam preparation

Designed for purchase by adults, suggesting a self-paced learning environment suitable for independent study

Explores topics such as parametric equations and numerical methods, which are essential components of A-Level mathematics

Builds upon the content covered in the Pure (Year 1 / AS) course, indicating a sequential learning path for A-Level students

Requires familiarity with differentiation techniques learned in the Pure (Year 1 / AS) course, suggesting a need for prior knowledge

Reviews summary

Comprehensive a-level pure maths year 2

According to students, this A-Level Maths: Pure (Year 2) course is a largely positive and comprehensive resource for studying the subject. Learners particularly praise the clarity of the explanations provided in the video lectures, which help make complex topics understandable. The course is also highlighted for its usefulness for exam preparation, with many students finding the practice materials, including quizzes and worksheets taken from past papers, to be highly valuable. The instructor's support in the Q&A section is also frequently mentioned as being helpful and responsive.

Instructor provides helpful Q&A support.

"Asked a question in the Q&A and got a clear, helpful response quickly."

"The instructor is active in the Q&A and helps when you get stuck."

"Support is good; questions are answered promptly and effectively."

"Really appreciate the help available in the Q&A section."

Highly relevant for A-Level exams.

"Used this course to revise for my A-Levels and it was perfect preparation."

"This course is tailored perfectly for the A-Level exams."

"Felt much more confident tackling exam questions after completing this course."

"Excellent for exam board specifications, covers everything needed."

Quizzes and worksheets are great practice.

"The quizzes after each section and the end-of-chapter worksheets with mark schemes are invaluable for practice."

"Practicing with the past paper questions provided was very helpful for solidifying understanding."

"Really liked the quizzes and worksheets; they are essential for testing knowledge."

"The included practice questions felt very relevant to actual exam style."

Covers the A-Level Pure Year 2 syllabus.

"This course covers the entire Year 2 Pure Maths syllabus thoroughly."

"It seems to cover all the required topics for A-Level Pure Maths Year 2."

"Comprehensive coverage of all the pure maths topics for the second year."

"Every topic listed in the syllabus is explained in detail."

Instructor explains concepts clearly.

"The lecturer has a very clear way of explaining complex topics, making them easy to follow."

"Found the explanations in the videos to be excellent and easy to understand."

"He explains everything in such a clear manner. I finally get partial fractions!"

"Woody explains things with perfect clarity and covers everything you need."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in A-Level Maths: Pure (Year 2) with these activities:

Review Trigonometric Identities

Show steps

Solidify your understanding of trigonometric identities before tackling advanced topics. This will make learning new identities and solving complex equations much easier.

Browse courses on Trigonometric Identities

Show steps

Review the definitions of sine, cosine, and tangent.
Practice proving basic trigonometric identities.
Work through example problems involving trigonometric equations.

Review: A-Level Mathematics for Edexcel: Pure Mathematics Year 2

Show steps

Use this book to supplement the course material and gain a deeper understanding of the concepts. This will help you prepare for exams and improve your overall performance.

View New A-Level Maths for Edexcel: Year 1 & 2... on Amazon

Show steps

Read the relevant chapters in the book that correspond to the course topics.
Work through the worked examples to understand the problem-solving techniques.
Attempt the practice questions and check your answers against the solutions.
Identify areas where you need further clarification and seek help from the instructor or other resources.

Practice Differentiation Problems

Show steps

Reinforce your differentiation skills through repetitive practice. This will help you master the chain rule, product rule, and quotient rule.

Show steps

Gather a set of differentiation problems from textbooks or online resources.
Solve each problem, showing all steps clearly.
Check your answers against the solutions and identify areas for improvement.
Repeat the process with increasingly complex problems.

Three other activities

Expand to see all activities and additional details

Show all six activities

Create a Trigonometry Cheat Sheet

Show steps

Consolidate your knowledge of trigonometric functions and identities by creating a comprehensive cheat sheet. This will serve as a valuable reference tool for future problem-solving.

Show steps

Gather all relevant formulas and identities related to trigonometry.
Organize the information logically and concisely.
Design the cheat sheet for easy readability and quick reference.
Share your cheat sheet with peers for feedback and improvement.

Review: Advanced Problems in Mathematics

Show steps

Enhance your problem-solving abilities by working through challenging problems. This will prepare you for tackling complex exam questions.

View Advanced Problems in Mathematics: Preparing for... on Amazon

Show steps

Select a set of problems from the book that align with the course topics.
Attempt to solve each problem independently.
Compare your solutions with the provided answers and explanations.
Analyze your mistakes and learn from them.

Model a Real-World Scenario with Parametric Equations

Show steps

Apply your knowledge of parametric equations to model a real-world scenario. This will help you understand the practical applications of this mathematical concept.

Show steps

Choose a real-world scenario that can be modeled using parametric equations, such as projectile motion or the movement of a robotic arm.
Develop a mathematical model using parametric equations to represent the scenario.
Simulate the model using software or programming tools.
Analyze the results and draw conclusions about the scenario.

Career center

Learners who complete A-Level Maths: Pure (Year 2) will develop knowledge and skills that may be useful to these careers:

Math Teacher

A math teacher educates students in mathematical concepts and problem-solving. This role requires a deep understanding of mathematics. The A-Level Maths course provides a comprehensive review of advanced mathematical topics. Someone who wishes to pursue a career as a math teacher may find this course useful. It covers a wide range of topics, including calculus, trigonometry, and numerical methods. It helps you feel more confident in your knowledge of A-Level maths.

See salaries and explore the career path for Math Teacher

Actuary

An actuary assesses and manages financial risks by applying mathematical and statistical principles. Actuaries often work in insurance and finance. This role demands a robust mathematical foundation, and the A-Level Maths course helps build this foundation through its coverage of topics such as binomial expansion, sequences and series, and calculus. These techniques are used in actuarial modeling. Exposure to radians and trigonometry may strengthen an actuary candidate's problem-solving skills. This course helps you learn important A-Level maths.

See salaries and explore the career path for Actuary

Statistician

A statistician collects, analyzes, and interprets numerical data. Statisticians use this to solve problems and answer questions across a variety of different industries. It requires a strong mathematical background, and the A-Level Maths course may help a statistician candidate. The course covers topics that statisticians use, such as trigonometric functions, which includes secant, cosecant, and cotangent, as well as vectors.

See salaries and explore the career path for Statistician

Game Developer

Game developers create video games for computers, consoles, and mobile devices. This profession typically requires mathematical skills. Since games use transformations and computer graphics, the A-Level Maths course's material on graphs and functions may prove useful. And because game physics relies on vectors and modelling, the sections covering calculus may be useful to someone who wants to make games.

See salaries and explore the career path for Game Developer

Machine Learning Engineer

A machine learning engineer develops and implements machine learning algorithms. These engineers require a strong foundation in mathematics, including calculus, linear algebra, and statistics. The A-Level Maths course helps one learn topics that can be found in machine learning. The calculus content is particularly relevant for optimizing models using gradient descent. Someone wishing to become a machine learning engineer may use this A-Level Maths course to build knowledge of relevant mathematics.

See salaries and explore the career path for Machine Learning Engineer

Economist

An economist studies the production, distribution, and consumption of goods and services. This role involves analyzing economic data and developing models. A strong foundation in mathematics is critical for success in this field. The course provides a review of calculus, functions, and graphs. These are useful for understanding economic models and relationships. This A-Level Maths course provides a thorough review of advanced topics, which helps those who aim to become economists.

See salaries and explore the career path for Economist

Aerospace Engineer

An aerospace engineer designs and develops aircraft, spacecraft, and related systems. This requires a strong foundation in mathematics. The A-Level Maths course includes vectors and calculus, which are important for understanding aerodynamics and orbital mechanics. Furthermore, the course covers functions and graphs, which are useful for modeling complex systems. This course goes over key information that can be useful for a future aerospace engineer.

See salaries and explore the career path for Aerospace Engineer

Financial Analyst

A financial analyst evaluates financial data, provides investment recommendations, and manages financial risk. This role requires a strong analytical and mathematical background. With the A-Level Maths course, you may boost your knowledge of sequences and series, which is useful when you want to understand growth patterns in financial markets. Additionally, a knowledge of functions, graphs, and calculus provides a deeper understanding of financial models. While more specialized knowledge is normally needed, this course focuses heavily on mathematics.

See salaries and explore the career path for Financial Analyst

Data Analyst

A data analyst collects, processes, and analyzes data to identify trends and insights. This career involves using mathematical and statistical techniques to interpret data. The A-Level Maths course may help to improve understanding of functions and graphs. This can strengthen a data analyst's capacity to visualize and interpret data. Additionally, the focus on sequences and series may support the analysis of trends over time. A data analyst often needs a bachelor's degree.

See salaries and explore the career path for Data Analyst

Data Scientist

A data scientist analyzes complex data sets to extract meaningful insights and inform business decisions. This career often involves using advanced mathematical and statistical techniques. A solid comprehension of topics such as binomial expansion and numerical methods helps a data scientist build and interpret models. Furthermore, understanding functions and graphs, including modulus functions and graph transformations, allows a data scientist to visualize and understand complex data relationships. This A-Level Maths course may provide a foundation for the mathematical skills necessary in data science.

See salaries and explore the career path for Data Scientist

Research Scientist

A research scientist conducts experiments and analyzes data to investigate scientific phenomena. This career often requires advanced mathematical skills. The A-Level Maths course provides exposure to functions, graphs, calculus, and numerical methods. These strengthen the analytic capabilities of a candidate for a research scientist position. The course's overview of trigonometry and vectors is helpful for research involving physics or engineering. If the course material is unfamiliar, it may be useful to learn the information this course teaches.

See salaries and explore the career path for Research Scientist

Civil Engineer

A civil engineer designs, constructs, and maintains infrastructure projects. This profession requires a strong understanding of mathematical principles. The A-Level Maths course helps to support the mathematical skills needed for this role. The course's coverage of trigonometry, vectors, and calculus is helpful for structural analysis and design. Moreover, the material on functions and graphs, including graph transformations, may strengthen the understanding of engineering models. Civil engineers typically need a bachelor's degree.

See salaries and explore the career path for Civil Engineer

Software Engineer

A software engineer designs, develops, and tests software applications. This career path relies on knowledge of mathematical principles. A strong foundation in calculus is helpful for optimizing algorithms, while skills in numerical methods are relevant for solving complex computational problems. The course's material on functions, graphs, and vectors is helpful for software engineers. With this course, prospective software engineers may gain a solid mathematical foundation for their future work.

See salaries and explore the career path for Software Engineer

Market Research Analyst

A market research analyst studies market conditions to assess the potential sales of a product or service. This position often involves analyzing data and trends. The A-Level Maths course may improve the analyst's understanding of sequences and series, which is useful for forecasting and trend analysis. The comprehension of functions and graphs may strengthen one's ability to visualize and interpret market data. It may also be useful for understanding how markets change over time.

See salaries and explore the career path for Market Research Analyst

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in A-Level Maths: Pure (Year 2).

A-Level Mathematics

Save

Is specifically designed for the Edexcel A-Level Mathematics syllabus and covers the Pure Mathematics Year 2 content. It provides clear explanations, worked examples, and practice questions. This book useful reference tool and can be used as a textbook for students following the Edexcel curriculum. It adds more depth to the existing course by providing additional examples and practice problems.

New A-Level Maths for Edexcel: Year 1 & 2 Complete...

Paperback

Advanced Problems in Mathematics: Preparing for...

Save

Provides a challenging collection of problems designed to stretch and develop mathematical skills. It is particularly useful for students aiming for top grades in A-Level mathematics. While not a core textbook, it offers excellent practice material and helps to deepen understanding of the concepts covered in the course. It is valuable as additional reading to solidify knowledge.

Advanced Problems in Mathematics: Preparing for...

Paperback

Advanced Problems in Mathematics: Preparing for...

Paperback

A-Level Maths

Pure (Year 2)

What's inside

Learning objectives

Syllabus

Good to know

Save this course

Reviews summary

Comprehensive a-level pure maths year 2

Activities

Career center

Reading list

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